A 7.80-g bullet moving at 570 m/spenetrates a tree trunk to a depth of 6.1 cm. (

Question

A 7.80-g bullet moving at 570 m/spenetrates a tree trunk to a depth of 6.1 cm. (a) Use work and energy considerations to findthe average frictional force that stops the bullet.
1 N

(b) Assuming the friction force is constant, determine how muchtime elapses between the moment the bullet enters the tree and themoment it stops moving.
2
(a) Use work and energy considerations to findthe average frictional force that stops the bullet.
1 N

(b) Assuming the friction force is constant, determine how muchtime elapses between the moment the bullet enters the tree and themoment it stops moving.
2

Explanation / Answer

(a) Let the average frictional forceacting on the bullet be F.

Work done against the frictionalforce as the bullet moves inside the block = F d

Initial total energy of the bullet= its kinetic energy = ½ m v^2

By conservation ofenergy,

F d = ½ mv2

F = ½ m v2/ d

where d = 6.1 cm = 0.061m.

F = ½ m v2/ d = ½ * 0.0078 * 570^2 / 0.061 = 20772.3

(b) Newton’s second law: F = ma where ‘a’ is the deceleration of thebullet.

20772.3 = 0.0078 a

a = 2.7 x 106m/s2

Use v = u + at to find the timeelapsed.

0 = 570 - 2.7 x 106 t

t = ....

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